Question

(a) State Faraday’s law of electromagnetic induction and explain the role of the negative sign in its expression.
(b) Explain, with an example, that Lenz’s law is consistent with the law of conservation of energy.

Hint:

For electromagnetic induction problems: - Faraday’s law gives the magnitude of induced EMF: \( \mathcal{E} = -\frac{d\Phi_B}{dt} \). - Lenz’s law (negative sign) ensures the induced current opposes the flux change, aligning with energy conservation.

Answer 1

(a): Faraday’s law and the negative sign.
Faraday’s law of electromagnetic induction states that the induced electromotive force (EMF) in a circuit is proportional to the rate of change of magnetic flux through the circuit: \[ \mathcal{E} = -\frac{d\Phi_B}{dt}, \] where \( \mathcal{E} \) is the induced EMF, and \( \Phi_B \) is the magnetic flux.
The negative sign reflects Lenz’s law, which states that the induced current opposes the change in magnetic flux that caused it. This opposition ensures that the system adheres to the conservation of energy, as the induced current works against the external change, requiring energy input to sustain the process. (b): Lenz’s law and conservation of energy .
Lenz’s law states that the induced current opposes the change in magnetic flux. This opposition ensures energy conservation because the energy to produce the induced current comes from work done against the opposing force.
Example: Consider a magnet approaching a conducting loop with its north pole. As the magnet moves closer, the magnetic flux through the loop increases. By Lenz’s law, the induced current in the loop creates a magnetic field opposing the magnet’s field (a north pole facing the approaching north pole). This induces a repulsive force, requiring external work to push the magnet closer. The work done is converted into electrical energy in the loop, thus conserving energy.